Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency service. For most of the year, calls arrive randomly at a rate of six a day. The time he takes to travel to a call and do the repair is randomly distributed with a mean of 90 minutes.
Forecasts for February suggest cold weather and last time this happened Piotr received emergency calls at a rate of 18 a day. Because of repeat business, Piotr is anxious not to lose a customer and wants the average waiting time to be no longer in February than during a normal month. How many assistants should he employ to achieve this?